Carlos del-Castillo-Negrete, Rylan Spence, Troy Butler, Clint Dawson
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引用次数: 0
摘要
我们提出了一种在数据一致(DC)框架内生成序列参数估计并量化动态系统中认识不确定性的新方法。数据一致性框架不同于传统的贝叶斯方法,因为它结合了初始密度的前推,在参数方向上进行选择性正则化,而在更新后的密度中,数据并未提供相关信息。这项研究扩展了之前的研究,将线性高斯理论纳入了 DC 框架,并引入了最大更新密度(MUD)估计,作为最小二乘法和最大后验(MAP)估计的替代方法。在这项工作中,我们介绍了 MUD 估计的实际或接近实时的操作设置算法,在这种情况下,空间-时间数据包以数据包的形式到达,以提供参数的更新估计并识别潜在的参数漂移。DC 框架内的计算诊断对于评估 (1) DC 更新和 MUD 估计的质量以及 (2) 参数值漂移的检测至关重要。这些算法被应用于估算:(1) 高保真风暴潮模型中的风阻参数;(2) 热传导问题中的热扩散场;(3) 流行病学模型中不断变化的感染率和潜伏率。
Sequential Maximal Updated Density Parameter Estimation for Dynamical Systems with Parameter Drift
We present a novel method for generating sequential parameter estimates and
quantifying epistemic uncertainty in dynamical systems within a data-consistent
(DC) framework. The DC framework differs from traditional Bayesian approaches
due to the incorporation of the push-forward of an initial density, which
performs selective regularization in parameter directions not informed by the
data in the resulting updated density. This extends a previous study that
included the linear Gaussian theory within the DC framework and introduced the
maximal updated density (MUD) estimate as an alternative to both least squares
and maximum a posterior (MAP) estimates. In this work, we introduce algorithms
for operational settings of MUD estimation in real or near-real time where
spatio-temporal datasets arrive in packets to provide updated estimates of
parameters and identify potential parameter drift. Computational diagnostics
within the DC framework prove critical for evaluating (1) the quality of the DC
update and MUD estimate and (2) the detection of parameter value drift. The
algorithms are applied to estimate (1) wind drag parameters in a high-fidelity
storm surge model, (2) thermal diffusivity field for a heat conductivity
problem, and (3) changing infection and incubation rates of an epidemiological
model.